HITC Sport understands that teenagers are already in London.
We can reveal that both players obtained their visas earlier this week and arrived in London on Saturday and are due to spend the next ten days with The Hammers.
The 18-year-old pair are understood to be on the radar of a host of top European clubs, but West Ham have used their scouting presence in the area to line up the pair.
Lambert, a tall yet elegant midfielder, is just leaving high school whilst striker Murray is with Waterhouse FC.
Both players are part of Jamaica's Under 20 team - coached by former Bolton star Ricardo Gardner - but have been tipped to get get called up to the main squad for this summer's Copa America for which the Reggae Boyz have again been invited to compete in this summer.